Problem solving with algebraic manipulation

12 questions

1. Evaluate the expression \frac{3x}{2x + 5} for x = 5.
2. Evaluate the expression \frac{x}{x + 1} for x = 19. Give your answer as a decimal.
3. A book store sells a book for £25, which is 25% more than its cost price. Which of these calculates cost price, p, of the book?
4. Expand and simplify 4(x - 2) - 2(3x + 4)
5. Simplify the expression \frac{x^2 - 9}{x - 3}
6. Fully factorise the expression 2x^2 + 12x
7. A right triangle has area 24 cm^2 and side lengths x and x + 2. What is the value of x?
8. The sum of two consecutive odd integers is 156. What are the two integers?
9. What is the positive value of x where (x + 4)(x - 2) = 0?
10. The difference between the square of a positive integer and the integer itself is 110. What is the integer?
11. The sum of the squares of two consecutive positive integers is 365. What is the smallest integer?
12. The product of two consecutive integers is 272. What are the two integers?

License: OGL